Question

Compound interest on a certain sum of money for 2 years at a rate of 'r' per cent per annum (compounding annually) is Rs. 8385. Simple interest on the same sum at the same rate for 2 years is Rs 7800. What is the value of r?
1. 15 percent
2. 12 percent
3. 18 percent
4. 16 percent

Answer 1

Correct Answer - Option 1 : 15 percent

Given:

In case of Compound Interest:

Time = 2 yrs, Rate = r% per annum compounded annually & Compound Interest = Rs. 8385

In case of Simple Interest:

T = 2 years, R = r% per annum & Simple Interest = Rs. 7800

Calculation:

Given that simple interest for 2 years = Rs. 7800

i.e., Simple interest for 1^st year is Rs. 3900 and simple interest for 2^nd year is also Rs. 3900

Now, 

Compound interest for 1^st year will be Rs. 3900

and compound interest for 2^nd year = 8385 - 3900

⇒ Rs. 4485

We can see that compound interest for 2^nd year is more than simple interest for 2^nd year by 4485 - 3900

⇒ Rs. 585

Now, Rs. 585 is the interest obtained for Rs. 3900 for 1 year.

So, Interest = (P × r × T)/100

⇒ 585 = (3900 × r × 1)/100

⇒ r = (585 × 100)/3900

⇒ r = 585/39

⇒ r = 15

∴ The value of r is 15%.